Sol. The pressure in the cylinder is due to the weight of the piston and remains constant. Assuming a frictionless seal (this is always done unless information is given to the contrary), a force balance provides

mg = PA – P atm A

(50) (9.81) = (P – 100000)

∴ P = 151600 Pa

The atmospheric pressure is included so that absolute pressure results. The volume at the initial state 1 is given as

V 1 = 100 × 10 –6 = 10 –4 m 3 Using v 1 at 60ºC, the mass is calculated to be

M = = = 0.09833 kg

At state 2 the temperature is 200ºC and the pressure is 0.15 MPa (this pressure is within 1 percent of the pressure of 0.1516 MPa, so it is acceptable). The volume is then

V 2 = mv 2 = (0.09833) (1.444) = 0.1420 m

3 Finally, the work is calculated to be

W = P(V 2 – V 1 ) = 151(600) (0.1420 – 0.0001) = 21500 J or 21.5 kJ